You mean as in putting your images on a webserver somewhere? I'm not sure I understand. If people are going to download your game, then they would expect to have the images in the download. If your game is going to be hosted on a website, then wouldn't that website be the place to put your images?
I also do not really understand what you mean by dragging images to the browser. Are you doing that to get the full path name to your images? You can use relative paths too. For example, if my game was "C:\Example\example.html" and one of my images is "C:\Example\images\image01.png" then in my game, I can use
<img src="images/image01.png">
to load it.
If that's not working for you, then it's probably because you're using test builds, in which case a temporary html file is created (I'm not sure where, and doubly so if you're using the web version of Twine) so you need the full file paths for the images. If that's the case, you can try this:
JavaScript:
Config.passages.onProcess = function (p) {
/* assuming you use <img src="images/whatever.png"> in your code and the actual folder containing the images are C:\Example\images\ */
return p.text.replace('src="images', 'src="C:/Example/images');
};
This is just a simple search and replace that the SugarCube engine will do on your code before parsing it. It should be put in your story's javascript section. Obviously, you should remove this before releasing your game because players are not going to keep the game in the same drives/folders as you.